Finite Group Databasebeta

← #98803

Subgroups — #98803

Order 512.

664 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14699C211yesmaximal, characteristic
2#10832C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4C2×#1271C212yesmaximal
5#7025C212yesmaximal
6C22×C4⋊C8—21no—
7C2×#389C411yescharacteristic
8C2×#389C2211yescharacteristic
9C2×#387—21no—
10C2×C43C2211yescharacteristic
11C2×#336—21no—
12C2×#336—21no—
13C2×#336—21no—
14C2×#336C2212yes—
15C2×#336C2212yes—
16#1436—21no—
17#1436—21no—
18C4⋊#95C411yescharacteristic
19C4⋊#95C411yescharacteristic
20C4⋊#95C411yescharacteristic
21C4⋊#95C2211yescharacteristic
22#1434—21no—
23#1271—24no—
24C23×C8—22no—
25C23×C8—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C42C2×C411yescharacteristic
33C22×C42C2×C411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42D411yescharacteristic
38C22×C42C2311yescharacteristic
39C2×C4⋊C8—24no—
40C2×C4⋊C8—42no—
41C2×C4⋊C8—42no—
42#389—21no—
43#389—21no—
44#389—42no—
45#389D412yes—
46#389Q812yes—
47#387—42no—
48#387—42no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C43—42no—
60#336—24no—
61#336—22no—
62#336—22no—
63#336—22no—
64#336—22no—
65#336—42no—
66#336—42no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22×C411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C22×C8—24no—
79C22×C8—24no—
80C22×C8—42no—
81C22×C8—42no—
82C22×C8—42no—
83C22×C8—42no—
84C22×C8—42no—
85C22×C8—42no—
86C22×C8—42no—
87C22×C8—42no—
88C22×C8—42no—
89C22×C8—42no—
90C22×C8—42no—
91C22×C8—42no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4C4⋊C412yes—
114C2×C4⋊C4C4⋊C412yes—
115C2×C42—22no—
116C2×C42—22no—
117C2×C42—22no—
118C2×C42—22no—
119C2×C42—22no—
120C2×C42—22no—
121C2×C42—22no—
122C2×C42—22no—
123C2×C42—22no—
124C2×C42—21no—
125C2×C42—22no—
126C2×C42—21no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42D812yes—
136C2×C42SD1612yes—
137C2×C42C2×D411yescharacteristic
138C2×C42C2×Q811yescharacteristic
139C2×C42#4111yescharacteristic
140C2×C42#4111yescharacteristic
141C4⋊C8—48no—
142#95—22no—
143#95—22no—
144#95—42no—
145#95—42no—
146#95—42no—
147#95—42no—
148#95—42no—
149#95—42no—
150#95—42no—
151#95—41no—
152#95—41no—
153#95—42no—
154C24C2×C22⋊C411yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4#9912yes—
218C22×C4#10112yes—
219C22×C4#10212yes—
220C22×C4#10212yes—
221C22×C4#10412yes—
222C22×C4#10412yes—
223C22×C4C2×C4⋊C411yescharacteristic
224C22×C4#11711yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4C22⋊Q811yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4#13112yes—
230C22×C4#13112yes—
231C22×C4C2×D811yescharacteristic
232C22×C4C2×SD1611yescharacteristic
233C22×C4#13512yes—
234C22×C4AGL(1,ℤ/8)11yescharacteristic
235C22×C4#13711yescharacteristic
236C22×C4#13712yes—
237C2×C8—44no—
238C2×C8—44no—
239C2×C8—44no—
240C2×C8—44no—
241C2×C8—44no—
242C2×C8—44no—
243C2×C8—82no—
244C2×C8—82no—
245C2×C8—82no—
246C2×C8—82no—
247C2×C8—82no—
248C2×C8—82no—
249C2×C8—82no—
250C2×C8—82no—
251C4⋊C4—24no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—82no—
260C4⋊C4—82no—
261C4⋊C4—84no—
262C42—24no—
263C42—24no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—44no—
269C42—44no—
270C42—44no—
271C42—44no—
272C42—42no—
273C42—42no—
274C23#38011yescharacteristic
275C23#40811yescharacteristic
276C23#40811yescharacteristic
277C23C2×#9911yescharacteristic
278C23#41011yescharacteristic
279C23C2×#10111yescharacteristic
280C23#41311yescharacteristic
281C23C2×#10211yescharacteristic
282C23#41611yescharacteristic
283C23#41711yescharacteristic
284C23#41911yescharacteristic
285C23C2×#10411yescharacteristic
286C23C2×#10411yescharacteristic
287C23#42111yescharacteristic
288C23#42111yescharacteristic
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4#32714yes—
373C2×C4#42412yes—
374C2×C4#43312yes—
375C2×C4#45911yescharacteristic
376C2×C4#46111yescharacteristic
377C2×C4#46412yes—
378C2×C4#47411yescharacteristic
379C2×C4#47611yescharacteristic
380C2×C4#47912yes—
381C8—84no—
382C8—84no—
383C22#146811yescharacteristic
384C22#147011yescharacteristic
385C22#147211yescharacteristic
386C22#147311yescharacteristic
387C22#148011yescharacteristic
388C22#148211yescharacteristic
389C22#148311yescharacteristic
390C22#148511yescharacteristic
391C22#149211yescharacteristic
392C22#149411yescharacteristic
393C22#149511yescharacteristic
394C22#149711yescharacteristic
395C22C2×#32711yescharacteristic
396C22#150011yescharacteristic
397C22#150811yescharacteristic
398C22#150911yescharacteristic
399C22#151311yescharacteristic
400C22#151511yescharacteristic
401C22#151611yescharacteristic
402C22#151711yescharacteristic
403C22#152611yescharacteristic
404C22#153211yescharacteristic
405C22#153211yescharacteristic
406C22#153411yescharacteristic
407C22#154011yescharacteristic
408C22#154611yescharacteristic
409C22#155211yescharacteristic
410C22#155911yescharacteristic
411C22#179811yescharacteristic
412C22#179911yescharacteristic
413C22#180111yescharacteristic
414C22#180211yescharacteristic
415C22#180511yescharacteristic
416C22#180611yescharacteristic
417C22#180611yescharacteristic
418C4—22no—
419C4—22no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—22no—
425C4—22no—
426C4—24no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—82no—
431C4—82no—
432C4—161no—
433C4—161no—
434C2#765411yescharacteristic
435C2#766611yescharacteristic
436C2#767711yescharacteristic
437C2#768511yescharacteristic
438C2#770111yescharacteristic
439C2#771311yescharacteristic
440C2#772311yescharacteristic
441C2#773111yescharacteristic
442C2#856211yescharacteristic
443C2#856711yescharacteristic
444C2#857011yescharacteristic
445C2#857111yescharacteristic
446C2#857411yescharacteristic
447C2#858411yescharacteristic
448C2#858911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#146992
#108322
#107952
C2×#12712
#70252